This paper addresses the system throughput maximization problem for HAPS third generation cellular systems. We assume that the Stratospheric Platform is able to perform a perfect link gain estimation for all mobile terminals, such that a centralized resource allocation strategy is made possible. A classical 3G wireless scenario is considered, where traffics characterized by different bit rates coexist with Best Effort Traffic services without stringent bit rate constraints. In this scenario, we firstly envisage three Rate Assignment schemes for best effort terminals which aim at achieving the maximum system throughput subject to different bit rate constraints. For the second envisaged rate assignment scheme, which represents the best compromise between service fairness and throughput, we then propose a simplified approach that allows to noticeably decrease the implementation complexity with a slight performance degradation.